(Optional, requires appendix) Return to Exercise S14. Assume, reasonably, that the probability of a lemon’s breaking down increases over the length of the road trip. Specifically, let q 5 m(m 1 500),...

(Optional, requires appendix) Return to Exercise S14. Assume, reasonably, that the probability of a lemon’s breaking down increases over the length of the road trip. Specifically, let q 5 m(m 1 500), where m is the number of miles in the round trip.

(a) Find the minimum integer number of miles, m, necessary to avoid the collapse of the market for oranges. That is, what is the smallest m such that the seller of an orange is willing to sell her car at the market price for a Citrus that has successfully completed the road trip?

(b) What is the minimum integer number of miles, m, necessary to achieve complete separation between functioning markets for oranges and lemons? That is, what is the smallest m such that the owner of a lemon will never decide to attempt the road trip?